Nope, the way it works is there's a directory somewhere in the file (typically at the end, but according to the spec it can be anywhere... I wonder if I'd screw some programs up by putting it at the beginning) that lists all the lumps and has pointers to where in the file they begin, as well as their sizes.
So as long as the offsets in the wadfile directory are correct, there won't be problems. Texture sizes wouldn't make a difference there because textures themselves aren't even lumps, and if you meant patches, they're stored the same way all lumps are stored, so they could be any size.
The reason flats are 64x64 and 128x128 and so on? I don't know exactly, it probably has to do with how they're drawn, or maybe the size. Flats are stored as bmps without headers, so they don't have any size information. If you keep them square, you can take the square root of the lump length to find the dimensions.
Textures have to have widths that are powers of 2 because of how the TEXTURE1 entries are stored. The heights don't have to be powers of 2. There are a few SRB2 textures with weird heights, I think.